ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: Martchenko, B., Institute of Electrodynamics of the Ukrainian national Academy of Sciences, Kiev-57, Ukraine Concerning on a theorem for periodic in Slutskiy sense linear random processes In the report the linear random process that may be represented by stochastic integral

ξ(t) = ∫_{−∞}^{∞} φ(τ, t)dη(τ),

where φ(τ, t) ∈ L_{2}(−∞, ∞) is a non-stochastic kernel on for every fixed t ∈ (−∞, ∞), η(τ), τ ∈ (−∞, ∞) is a stochastically continuous generating process with independent increments is discussed. The main theorem that determines the necessary and sufficient conditions imposed on the kernel and the generating process in order that ξ(t) be T-periodic process in Slutskiy sense is formulated. Applications aspects and practical significance of the theorem are discussed